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december 2014 A new proof for the bornologicity of the space of slowly increasing functions
Julian Larcher, Jochen Wengenroth
Bull. Belg. Math. Soc. Simon Stevin 21(5): 887-894 (december 2014). DOI: 10.36045/bbms/1420071860

Abstract

A. Grothendieck proved at the end of his thesis that the space $\mathcal{O}_M$ of slowly increasing functions and the space $\mathcal{O}_{C}'$ of rapidly decreasing distributions are bornological. Grothendieck's proof relies on the isomorphy of these spaces to a sequence space and we present the first proof that does not utilize this fact by using homological methods and, in particular, the derived projective limit functor.

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Julian Larcher. Jochen Wengenroth. "A new proof for the bornologicity of the space of slowly increasing functions." Bull. Belg. Math. Soc. Simon Stevin 21 (5) 887 - 894, december 2014. https://doi.org/10.36045/bbms/1420071860

Information

Published: december 2014
First available in Project Euclid: 1 January 2015

zbMATH: 1331.46065
MathSciNet: MR3298484
Digital Object Identifier: 10.36045/bbms/1420071860

Subjects:
Primary: 46F05, 46M18
Secondary: 46A08, 46A45

Rights: Copyright © 2014 The Belgian Mathematical Society

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Vol.21 • No. 5 • december 2014
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